10 papers
Probing Structural Mathematical Reasoning in Language Models with Algebraic Trapdoors
Igor Rivin
We introduce a benchmark suite for evaluating structural mathematical reasoning in language models, built on subgroup-construction problems in SL(3, Z) with cryptographic-style ver…
DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale
Alexander Kolpakov, Igor Rivin
Dimensionality reduction methods such as UMAP and t-SNE are central tools for visualising high-dimensional data, but their local-neighborhood objectives can preserve sampling noise…
Linear recurrences and rational Lambert series
Igor Rivin
For a sequence , define \[ L_γ(z):=\sum_{n\ge 1}γ_n\frac{z^n}{1-z^n} =\sum_{n\ge 1}\Bigl(\sum_{d\mid n}γ_d\Bigr)z^n. \] We prove a short rigidity theorem: if…
Permanents of matrix ensembles: computation, distribution, and geometry
Igor Rivin
We report on a computational and experimental study of permanents. On the computational side, we use the GPU to greaatly accelerate the computation of permanents over …
Monte-Carlo Irreducibility and Imprimitivity Detection of Polynomials over
Igor Rivin
We study fast Monte-Carlo methods for testing irreducibility and detecting arithmetic imprimitivity of polynomials over . Building on the subset-sum criterion of Pemant…
Maximal Volume Ideal Polyhedra and the Arithmetic Angle Phenomenon
Igor Rivin
We present a software suite for the analysis and optimization of ideal convex polyhedra in hyperbolic 3-space . Using Rivin's variational characterization of ideal po…